Quantitative Analysis
Parallel Processing
Numerical Analysis
C++ Multithreading
Python for Excel
Python Utilities
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I. Basic math.
1. Conditional probability.
2. Normal distribution.
3. Brownian motion.
4. Poisson process.
5. Ito integral.
6. Ito calculus.
A. Example: exponential of stochastic process.
B. Example: integral of t_dW.
C. Example: integral of W_dW.
D. Example: integral of W_dt.
7. Change of measure.
8. Girsanov's theorem.
9. Forward Kolmogorov's equation.
10. Backward Kolmogorov's equation.
11. Optimal control, Bellman equation, Dynamic programming.
II. Pricing and Hedging.
III. Explicit techniques.
IV. Data Analysis.
V. Implementation tools.
VI. Basic Math II.
VII. Implementation tools II.
VIII. Bibliography
Notation. Index. Contents.

Example: integral of t_dW.

he goal of this section is to calculate distribution of MATH . By the property ( Ito isometry ) we have MATH The integral MATH is a limit of a sum of normal variables. Each of the variables has zero mean. Hence, the result is a normal variable with zero mean. We conclude,

MATH (Int t dW)
for some standard normal variable $\xi$ .

Notation. Index. Contents.

Copyright 2007